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college mathematics for business

Questions and Answers of College Mathematics For Business

Problem refer to Figures A–D. Set up definite integrals in Problem that represent the indicated shaded area.Shaded area in Figure D f(x) g(x) y = f(x) y = g(x) a a (A) (B) h(x) F(x) b a y = h(x) y
In Problem find the area bounded by the graphs of the indicated equations over the given interval.y = 5 - 2x - 6x2; y = 0, 1 ≤ x ≤ 2
In Problem find the area bounded by the graphs of the indicated equations over the given interval.y = 5x + 7; y = 12, -3 ≤ x ≤ 1
If you want to use integration by parts to find ∫(x + 1)5 (x + 2) dx, which is the better choice for u: u = (x + 1)5 or u = x + 2? Explain your choice and then integrate.
In Problem evaluate each definite integral to two decimal places. 30 500 e0.02 0.09(30-1) dt
Problem refer to Figures A–D. Set up definite integrals in Problem that represent the indicated shaded area.Explain why ∫ba h(x) dx does not represent the area between the graph of y = h(x) and
In Problem find the area bounded by the graphs of the indicated equations over the given interval.y = -x + 2; y = x2 + 3, -1 ≤ x ≤ 4
In Problem find the area bounded by the graphs of the indicated equations over the given interval. y = y = -e, 1 sIS 2
Problem are mixed—some require integration by parts, and others can be solved with techniques considered earlier. Integrate as indicated, assuming x > 0 whenever the natural logarithm function
In Problem explain which of (A), (B), and (C) are equal before evaluating the expressions. Then evaluate each expression to two decimal places. هر ک « سام( ] (A) e0.07(8-1) dt dt )0 0 - 56
In Problem explain which of (A), (B), and (C) are equal before evaluating the expressions. Then evaluate each expression to two decimal places. 10 (A) 2,000e0.05t 0.12(10-1) dt 10 (B)
In Problem find the area bounded by the graphs of the indicated equations over the given interval.y = x; y = -x3, -2 ≤ x ≤ 2
In Problem find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.y = x + 4; y = 0; 0 ≤ x ≤ 4
Problem are mixed—some require integration by parts, and others can be solved with techniques considered earlier. Integrate as indicated, assuming x > 0 whenever the natural logarithm function
In Problem find the area bounded by the graphs of the indicated equations over the given interval.y = x2; y = -x4; -2 ≤ x ≤ 2
In Problem use a graphing calculator to graph the normal probability density functionthat has the given mean μ and standard deviation σ.μ = 0, σ = 1 1 f(x) ||
In Problem find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.y = x2 - 20; y = 0; -3 ≤ x ≤ 0
In Problem use a graphing calculator to graph the normal probability density functionthat has the given mean μ and standard deviation σ.μ = 20, σ = 5 1 f(x) ||
In Problem use a graphing calculator to graph the normal probability density functionthat has the given mean μ and standard deviation σ.μ = 500, σ = 100 1 f(x) ||
In Problem find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.y = -x2 + 10; y = 0; -3 ≤ x ≤ 3
Problem are mixed—some require integration by parts, and others can be solved with techniques considered earlier. Integrate as indicated, assuming x > 0 whenever the natural logarithm function
In Problem set up definite integrals that represent the shaded areas in the figure over the indicated intervals.Interval [a, b] y = f(x) a с d y = g(x)
In Problem use a graphing calculator to graph the normal probability density functionthat has the given mean μ and standard deviation σ.μ = 300, σ = 25 1 f(x) ||
The weekly marginal cost of producing x pairs of tennis shoes is given by where C(x) is cost in dollars. If the fixed costs are $2,000 per week, find the cost function. What is the average cost
The rate at which the total number of sales is changing is given by S′(t) where t is the number of months since the product’s release. What does represent? 24 S'(t) dt 12
Find the amount A in an account after t years if dA = rA dt A(0) = 8,000 A(2) = 8,161.61
The rate at which the total amount of money put into an advertising campaign is changing is given by A′(t) where t is the number of days since the campaign began. What does represent? .7 A'(t) dt
The marginal average cost of producing x smart watches is given bywhere C ̅(x) is the average cost in dollars. Find the average cost function and the cost function. What are the fixed costs?
A company is trying to expose a new product to as many people as possible through TV ads. Suppose that the rate of exposure to new people is proportional to the number of those who have not seen the
Using production and geological data, the management of an oil company estimates that oil will be pumped from a field producing at a rate given bywhere R(t) is the rate of production (in thousands of
An automobile company is ready to introduce a new line of hybrid cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department
A company is trying to expose a new product to as many people as possible through online ads. Suppose that the rate of exposure to new people is proportional to the number of those who have not seen
The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of $1000 per unit [p(0) = 1000], and there is a weekly demand of 10 units
A defense contractor is starting production on a new missile control system. On the basis of data collected during assembly of the first 16 control systems, the production manager obtained the
A store orders 600 units of a product every 3 months. If the product is steadily depleted to 0 by the end of each 3 months, the inventory on hand I at any time t during the year is shown in the
For relatively clear bodies of water, the intensity of light is reduced according towhere I is the intensity of light at x feet below the surface. For the Sargasso Sea off the West Indies, k =
A contaminated lake is treated with a bactericide. The rate of increase in harmful bacteria t days after the treatment is given bywhere N(t) is the number of bacteria per milliliter of water. Since
Under certain assumptions, the blood pressure P in the largest artery in the human body (the aorta) changes between beats with respect to time t according towhere a is a constant. Find P = P(t) that
A yeast culture is growing at the rate of W′(t) = 0.2e0.1t grams per hour. If the starting culture weighs 4 grams, what will be the weight of the culture W(t) after t hours? After 8 hours?
Monthly sales of an SUV model are expected to increase at the rate ofS′(t) = -24t1/3SUVs per month, where t is time in months and S(t) is the number of SUVs sold each month. The company plans to
A single injection of a drug is administered to a patient. The amount Q in the body then decreases at a rate proportional to the amount present. For a particular drug, the rate is 4% per hour.
Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given bywhere R(t) is the rate of production (in thousands of
A community of 10,000 people is homogeneously mixed. One person who has just returned from another community has influenza. Assume that the home community has not had influenza shots and all are
The projected rate of increase in enrollment at a new college is estimated bywhere E(t) is the projected enrollment in t years. If enrollment is 2,000 now (t = 0), find the projected enrollment 15
For an average person, the rate of change of weight W (in pounds) with respect to height h (in inches) is given approximately byFind W(h) if W(60) = 108 pounds. Find the weight of an average person
A defense contractor is starting production on a new missile control system. On the basis of data collected during the assembly of the first 16 control systems, the production manager obtained the
The rate of growth of the population N(t) of a new city t years after its incorporation is estimated to beIf the population was 5,000 at the time of incorporation, find the population 9 years later.
A yeast culture weighing 2 grams is expected to grow at the rate of W′(t) = 0.2e0.1t grams per hour at a higher controlled temperature. How much will the weight of the culture increase during the
Public awareness of a congressional candidate before and after a successful campaign was approximated bywhere t is time in months after the campaign started and P(t) is the fraction of the number of
Sociologists have found that a rumor tends to spread at a rate in direct proportion to the number x who have heard it and to the number P - x who have not, where P is the total population (logistic
If the temperature in an aquarium (in degrees Celsius) is given byC(t) = t3 - 2t + 10 0 ≤ t ≤ 2over a 2-hour period, what is the average temperature over this period?
In Problem set up definite integrals that represent the shaded areas in the figure over the indicated intervals.Interval [a, b] y = f(x) a
In a study on small-group dynamics, sociologists found that when 10 members of a discussion group were ranked according to the number of times each participated, the number N(k) of times that the
In Problem round function values to four decimal places and the final answer to two decimal places.Use the trapezoidal rule with n = 3 to approximate L°V1 + x*dx
In Problem find the derivative of f(x) and the indefinite integral of g(x).f(x) = 5x; g(x) = x3
In Problem find real numbers b and c such that f(t) = ebect.f(t) = e5(4 - t)
In Problem set up definite integrals that represent the shaded areas in the figure over the indicated intervals.Interval [b, c] y = f(x) a
In Problem use geometric formulas to find the area between the graphs of y = f (x) and y = g(x) over the indicated interval.f(x) = 60, g(x) = 45; [2, 12]
In Problem round function values to four decimal places and the final answer to two decimal places.Use the trapezoidal rule with n = 2 to approximate SV1 + x*dx.
In Problem find the derivative of f(x) and the indefinite integral of g(x).f(x) = x2; g(x) = ex
In Problem set up definite integrals that represent the shaded areas in the figure over the indicated intervals.Interval [a, c] a y = f(x) b C X
In Problem find real numbers b and c such that f(t) = ebect.f(t) = e3(15 - t)
In Problem round function values to four decimal places and the final answer to two decimal places.Use the trapezoidal rule with n = 6 to approximate SV1 + x*dx
In Problem use geometric formulas to find the area between the graphs of y = f (x) and y = g(x) over the indicated interval.f(x) = -30, g(x) = 20; [-3, 6]
In Problem find the derivative of f(x) and the indefinite integral of g(x).f(x) = x3; g(x) = 5x
In Problem find real numbers b and c such that f(t) = ebect.f(t) = e0.04(8 - t)
In Problem use geometric formulas to find the area between the graphs of y = f (x) and y = g(x) over the indicated interval.f(x) = 6 + 2x, g(x) = 6 - x; [0, 5]
In Problem round function values to four decimal places and the final answer to two decimal places.Use the trapezoidal rule with n = 4 to approximate SV1 + x*dx
In Problem find the derivative of f(x) and the indefinite integral of g(x). f(x) = e;g(x)
In Problem find the derivative of f(x) and the indefinite integral of g(x).f(x) = ex; g(x) = x2
In Problem find real numbers b and c such that f(t) = ebect.f(t) = e0.02(12 - t)
In Problem use geometric formulas to find the area between the graphs of y = f (x) and y = g(x) over the indicated interval.f(x) = 0.5x, g(x) = 0.5x - 4; [0, 8]
In Problem find real numbers b and c such that f(t) = ebect.f(t) = e0.05t e0.08(20 - t)
In Problem find each indefinite integral and check the result by differentiating. dx J V2r - 2
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Unlimited growth:y = 5,250e0.12t0 ≤ t ≤ 100 ≤ y ≤ 20,000 Table 1 Exponential
A company manufactures downhill skis. The research department produced the marginal cost graph shown in the accompanying figure, where C′(x) is in dollars and x is the number of pairs of skis
For Problem use derivatives to determine whether f is increasing or decreasing on the given interval. Use L4 or R4, whichever is appropriate, to give an overestimate of the signed area on the given
In Problem find each indefinite integral and check the result by differentiating. dx V3x* + 1
In Problem find each indefinite integral. 2х dx
For Problem use derivatives to determine whether f is increasing or decreasing on the given interval. Use L4 or R4, whichever is appropriate, to give an overestimate of the signed area on the given
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Exponential decay:p = 100e-0.05x0 ≤ x ≤ 300 ≤ p ≤ 100 Table 1 Exponential
The mean value theorem states that if F(x) is a differentiable function on the interval [a, b], then there exists some number c between a and b such thatExplain why the mean value theorem implies
In Problem find each indefinite integral and check the result by differentiating. (In x)² xp-
For Problem use derivatives to determine whether f is increasing or decreasing on the given interval. Use L4 or R4, whichever is appropriate, to give an overestimate of the signed area on the given
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Exponential decay:p = 1,000e-0.08x0 ≤ x ≤ 400 ≤ p ≤ 1,000 Table 1 Exponential
The weekly marginal profit for an output of x units is given approximately byWhat is the total change in profit for a change in production from 10 units per week to 40 units? Set up a definite
In Problem find each indefinite integral and check the result by differentiating. et 2e - 1
In Problem the left sum Ln or the right sum Rn is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? (Each function is increasing over the
In Problem find each indefinite integral. xe – 2x dx
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Limited growth:N = 1,00(1 - e-0.05t)0 ≤ t ≤ 1000 ≤ N ≤ 100 Table 1 Exponential
A company manufactures mountain bikes. The research department produced the marginal cost functionwhere C′(x) is in dollars and x is the number of bikes produced per month. Compute the increase in
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Limited growth:N = 1,000(1 - e-0.07t)0 ≤ t ≤ 700 ≤ N ≤ 1,000 Table 1 Exponential
In Problem find each indefinite integral and check the result by differentiating. e dx
If the marginal profit for producing x units per day is given byP′(x) = 100 - 0.02x P(0) = 0where P(x) is the profit in dollars, find the profit function P and the profit on 10 units of production
An oil well starts out producing oil at the rate of 60,000 barrels of oil per year, but the production rate is expected to decrease by 4,000 barrels per year. Thus, if P(t) is the total production
In Problem find each indefinite integral and check the result by differentiating. In (x + 5) -dp- x + 5
In Problem the left sum Ln or the right sum Rn is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? (Each function is increasing over the
In Problems find the derivative or indefinite integral as indicated. d (6r? (6r2 – 7x + 2) dx dx
A new piece of industrial equipment will depreciate in value, rapidly at first and then less rapidly as time goes on. Suppose that the rate (in dollars per year) at which the book value of a new
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Logistic growth: 1,000 N = 1 + 999e 0.41 0 st< 40 0 < Ns 1,000

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